VARIANCE INFLATION FACTORS

Variance inflation factors are a measure of the multi-colinearity
in a regression design matrix (i.e., the independent variables).

Multi-colinearity results when the columns of X have significant
interdependence (i.e., one or more columns of X is close to a
linear combination of the other columns). Multi-colinearity
can result in numerically unstable estimates of the regression
coefficients (small changes in X can result in large changes
to the estimated regression coefficients).

Pairwise colinearity can be determined from viewing a correlation
matrix of the independent variables. However, correlation
matrices will not reveal higher order colinearity.

There are a number of approaches to dealing with
multi-colinearity. Some of these include:

Delete one or more of the independent variables from
the fit.

Perform a principal components regression.

Compute the regression using a singular value
decomposition approach. Note that Dataplot uses
a modified Gram-Schmidt method (Dataplot can perform
a singular value decomposition, however this has not
been incorporated into the fit).

Variance inflation factors are one measure that can be used to
detect multi-colinearity (condition indices are another).

Variance inflation factors are a scaled version of the
multiple correlation coefficient between variable j and
the rest of the independent variables. Specifically,

where Rj is the multiple correlation
coefficient.

Variance inflation factors are often given as the reciprocal
of the above formula. In this case, they are referred to
as the tolerances.

If Rj equals zero (i.e., no correlation
between Xj and the remaining independent
variables), then VIFj equals 1. This
is the minimum value. Neter, Wasserman, and Kutner (see
Reference below) recommend looking at the largest VIF value.
A value greater than 10 is an indiciation of potential
multi-colinearity problems.
Syntax:

LET <y1> = VARIANCE INFLATION FACTORS <mat1>
<SUBSET/EXCEPT/FOR qualification>
where <mat1> is the design matrix for which the variance
inflation factors are to be computed;
<y1> is a vector where the resulting variance
inflation factors are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is
optional (and rarely used in this context).

Examples:

LET Y = VARIANCE INFLATION FACTORS X

Note:

Matrices are created with either the READ MATRIX, CREATE MATRIX,
or MATRIX DEFINITION command. Enter HELP MATRIX DEFINITION,
HELP CREATE MATRIX, and HELP READ MATRIX for details.

Note:

The columns of a matrix are accessible as variables by appending an
index to the matrix name. For example, the 4x4 matrix C has
columns C1, C2, C3, and C4. These columns can be operated on like
any other DATAPLOT variable.

Note:

The maximum size matrix that DATAPLOT can handle is set when
DATAPLOT is built on a particular site. Enter the command
HELP MATRIX DIMENSION for details on the maximum size matrix
that can be accomodated.